1
Identities Formula
\[a^{2}-b^{2} \equiv (a+b)(a-b)\]
\[(a-b)^{2} \equiv a^{2} – 2ab + b^{2}\]
\[a^{3}-b^{3} \equiv (a-b)(a^{2} + ab + b^{2})\]
\[(a+b)^{2} \equiv a^{2} + 2ab + b^{2}\]
\[a^{3}+b^{3} \equiv (a+b)(a^{2} – ab + b^{2})\]
2
Law of Indices Formula
\[Given\:a, b \neq 0,\:m,\:n\:\epsilon\:\mathbb{Q}\] \[(To\:be\:ignored\:under\:secondary\:syllabus)\]
\[a^{m} \times a^{n} = a^{m + n}\]
\[\frac{a^{m}}{a^{n}} = a^{m – n} \]
\[(a^{m})^{n} = a^{m \times n}\]
\[a^{-1} = \frac{1}{a}\]
\[a^{-m} = \frac{1}{a^{m}}\]
\[(ab)^{m} = a^{m} \times b^{m}\]
\[(\frac{a}{b})^{m} = \frac{a^{m}}{b^{m}}\]
\[a^{0} = 1\]
\[a^{\frac{1}{m}} = \sqrt[m]{a}\]
\[(where\:m\:is\:a\:positive\:integer)\]
3
Statistical Topic
\[Mean \: (\bar{x}) = \frac{x_{1} + x_{2} + x_{3} + x_{4} + … + x_{n}}{n}\]
\[Median = (\frac{n + 1}{2})th \]
\[Standard \: Deviation \: (\sigma ) = \sqrt{\frac{(x_{1} – \bar{x})^{2} + (x_{2} – \bar{x})^{2} + (x_{3} – \bar{x})^{2} + … + (x_{n} – \bar{x})^{2}}{n}}\]
\[Varience = \frac{(x_{1} – \bar{x})^{2} + (x_{2} – \bar{x})^{2} + (x_{3} – \bar{x})^{2} + … + (x_{n} – \bar{x})^{2}}{n}\]
\[Standard \: Score = \frac{x_{n} – \bar{x}}{\sigma }\]
4
Trigonometry Identities Formula
\[\mathbf{Reciprocal \: Identities}\]
\[sin\:\theta = \frac{1}{csc\:\theta}\]
\[cos \: \theta = \frac{1}{sec \: \theta}\]
\[tan \: \theta = \frac{1}{cot \: \theta}\]
\[csc \: \theta = \frac{1}{sin \: \theta}\]
\[sec \: \theta = \frac{1}{cos \: \theta}\]
\[cot \: \theta = \frac{1}{tan \: \theta}\]
\[\mathbf{Confustion \: Identities:}\]
\[sin \: \theta = cos(\frac{\pi}{2} – \theta)\]
\[sec \: \theta = csc (\frac{\pi}{2}-\theta)\]
\[tan \: \theta = cot(\frac{\pi}{2}-\theta)\]
\[cos\:\theta=sin(\frac{\pi}{2}-\theta)\]
\[csc \: \theta = sec(\frac{\pi}{2}-\theta)\]
\[cot \: \theta = tan(\frac{\pi}{2}-\theta)\]
\[\mathbf{Pythagorean \: Identities:}\]
\[sin^{2} \: \theta + cos ^{2} \: \theta = 1\]
\[1 + tan ^{2} \: \theta = sec ^{2} \: \theta\]
\[1 + cot ^{2} \: \theta = csc ^{2} \: \theta\]
\[\mathbf{Even \: Odd \: Identities:}\]
\[sin(- \theta) = – sin \: \theta\]
\[tan(-\theta) = -tan \: \theta\]
\[cos(- \theta) = cos \: \theta\]
\[csc(-\theta) = -csc \: \theta\]
\[cot(-\theta) = – cot \: \theta\]
\[sec (-\theta) = sec\:\theta\]
\[\mathbf{Quotient \: Identities:}\]
\[tan \: \theta = \frac{sin \: \theta}{cos \: \theta}\]
\[cot \: \theta = \frac{cos \: \theta}{sin \: \theta}\]